Making Physics

A theory of Physics in order to be useful must provide values for certain physical quantities in definite circumstances. For this to be possible it is necessary a mathematical framework which will make the computation/presentation of these values possible. This framework has been discussed in the previous chapters. Let us recall these chapters briefly. We started with the independence of functions which led us to the definition of coordinate functions in a space (a manifold) and subsequently to the coordinate systems which characterize—that is, give identity—to the points of the space. In a given neighborhood of the space we defined various coordinate systems and related them with appropriate groups of coordinate transformations which made possible the selection of classes of coordinate systems.